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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Cell-like closed-$0$-dimensional decompositions of $R^{3}$ are $R^{4}$ factors

Authors: Robert D. Edwards and Richard T. Miller
Journal: Trans. Amer. Math. Soc. 215 (1976), 191-203
MSC: Primary 57A10
MathSciNet review: 0383411
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Abstract: It is proved that the product of a cell-like closed-0-dimensional upper semicontinuous decomposition of ${R^3}$ with a line is ${R^4}$. This establishes at once this feature for all the various dogbone-inspired decompositions of ${R^3}$. The proof makes use of an observation of L. Rubin that the universal cover of a wedge of circles admits a 1-1 immersion into the wedge crossed with ${R^1}$.

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Keywords: Closed-0-dimensional decomposition, cell-like decomposition, cube-with-handles, window building
Article copyright: © Copyright 1976 American Mathematical Society